Minimum-cost neuron selector

Read the equation

Sets the selector for neuron i to one when its cost equals the minimum available cost. If several neurons tie, this indicator can select several at once; a single-winner implementation needs a tie-breaking rule.

Terms & definitions

The recovered passage does not supply a separate symbol table. Read the source context for the notation used in this version; familiar letters may carry different meanings in other builds.

How it works

1. Read \rho_i(x) as the quantity being defined or updated by this relation.

2. Applies the stated minimum, maximum, or clamp. These bounds are part of the actual operation.

3. Use this version’s variable definitions and update order. The same symbol may be assigned a different meaning in another build.

Assumptions & limits

Source recovery establishes that the expression appears in this record. Its mathematical validity, implementation behavior, and interpretation must be assessed separately. See the linked source and research notes for the checks available for this version.

Original context

W_{ij} = \alpha C_i + \beta C_j

5. Routing (simple deterministic selector)

\rho_i(x) = \mathbf{1}(C_i = \min_j C_j)

This picks the cheapest neuron — NOT based on coherence, intent, awareness, or self-evaluation.

6. Task operator (safe functional tool)

Each neuron has a task operator:
T_i(x) = \mathcal{F}_i(x)

\rho_i(x) = \mathbf{1}(C_i = \min_j C_j)

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